Doug, it depends on its engineering. If it is brass, probably somewhere near 34". If it is an ABS plastic shell and on an engine costing between $80-$280, as low as 18" if the driver wheels are to scale and the engine is a N&W J Class.
Does the paperwork, if included, not tell you what the minimum radius is?
Maybe set up some flextrack curves, starting with 18", and see if you can get it to run smoothly around such curves forwards and backwards. Even so, will the passenger cars you intend to pull be happy with that radius?
As for realism, that is subjective. Someone very happy to be able to play with a nicely laid out train may find 18" curves are his dream. If you were to poll 100 people at random, no matter how familiar they are with the hobby and scale, you would get a range of answers. However, they would center around something like 28" being the lower end of what looks "realistic". Once you get radiu outward of 36", it looks quite natural.
One last thing: the higher above the curve your vantage point as you watch your tains on the curves, the worse it will seem. As your layout height rises and you find yourself watching as a real person would, trackside, you won't notice the tighter curves so much.
-Crandell